Question

If the value of \[\dfrac{a}{2b}=\dfrac{7}{4}\] find the value of \[\dfrac{a+2b}{a-2b}\]

Answer 1

Hint: To solve this question, we will use the concept of mathematics called components and dividends. According to it, the ratios of the number is also equal to the ratios of the number added by the number subtracted. We will use this concept to get the solution.

Complete step-by-step solution:
Given the value of \[\dfrac{a}{2b}=\dfrac{7}{4}\]
Then, we have to determine \[\dfrac{a+2b}{a-2b}\]
We will use the concept of components and dividends to solve this question.
It says “if the ratio of any two numbers is equal to the ratio of another two numbers then the ratio of the sum of numerator and denominator to the difference of numerator and denominator of both rational numbers are equal".
Example if \[\dfrac{a'}{b'}=\dfrac{c'}{d'}\] then \[\dfrac{a'+b'}{a'-b'}=\dfrac{c'+d’}{c’-d'}\] again here, we have \[\dfrac{a}{2b}=\dfrac{7}{4}\]
Then, applying the concept of components and dividends on the left side and right side, we get:
\[\Rightarrow \dfrac{a+2b}{a-2b}=\dfrac{7+4}{7-4}=\dfrac{11}{3}\]
Therefore, we have obtained that \[\Rightarrow \dfrac{a+2b}{a-2b}=\dfrac{11}{3}\] which is the required result.

Note: There is no other way to solve this question, other than using components and dividends. The possibility of a mistake in this question can be at the point where we are using a+2b in numerator and a-2b at the denominator. Be clear that, using a-2b in numerator and a+2b in the denominator will reverse the answer as $\dfrac{4}{7}$ and not $\dfrac{7}{4}$